On the nature of the phase transition triggered by vortex-like defects in the 2D ginzburg - Landau model

The two-dimensional lattice Ginzburg - Landau Hamiltonian is simulated numerically for different values of the coherence length ξ in units of the lattice spacing a, a parameter which controls amplitude fluctuations. The phase diagram on the plane T-ξ is measured. Amplitude fluctuations change dramatically the nature of the phase transition: For values of ξ/a ≃ 1, instead of the smooth Kosterlitz-Thouless transition there is a first-order transition with a discontinuity in the vortex density v and a sharper drop in the helicity modulus Γ. Both observables υ and Γ are analyzed in detail at the crossover region between first and second order which occurs for intermediate values of ξ/a.